As the title says, how do I solve inequalities like $||x|-3|\geq0$?
P.S. If the question seems invalid please correct me.
2026-04-11 21:54:44.1775944484
How do I solve inequalities like $||x|-3|\geq0$?
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Your example is always true since the absolute value function outputs always non-negative numbers.
As a training example, consider $$||x|-3|=2.$$ When is it equal to $2$? When the argument of the absolute value is $2$ or $-2$. $$|x|-2=2 \lor |x|-3=-2.$$ For the first equation move $-2$ to the right side. Then ask yourself: when is $|x|=4$? Now you should be able to answer that and then solve the other equation. The set of all possible values of x includes all of the deduced answers along the way.
For inequalities, to solve $|x| > a$ the argument must be greater than $a$ or smaller than $a$. To solve $|x|<a$ the argument must be smaller than $a$ and also greater than $-a$.